Finite Group Databasebeta

← #34082194

Subgroups — #34082194

Order 19328.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752947C211yesmaximal, characteristic, complemented
2#23752602C211yesmaximal, characteristic, complemented
3#23752599C211yesmaximal, characteristic, complemented
4#23752594C211yesmaximal, characteristic, complemented
5#23752434C211yesmaximal, characteristic, complemented
6#23752431C211yesmaximal, characteristic, complemented
7#23752427C211yesmaximal, characteristic, complemented
8#23752424C211yesmaximal, characteristic, complemented
9#23752407C211yesmaximal, characteristic, complemented
10#23752404C211yesmaximal, characteristic, complemented
11#23752343C211yesmaximal, characteristic, complemented
12#23752312C211yesmaximal, characteristic, complemented
13#23752310C211yesmaximal, characteristic, complemented
14C4×#14558989C211yesmaximal, characteristic, complemented
15#559×C151C211yesmaximal, characteristic, complemented
16C2×#14558994C2211yescharacteristic
17C2×#14558992C2211yescharacteristic
18C2×#14558992C2211yescharacteristic
19C2×#14558991C2211yescharacteristic
20C2×#14558991C2211yescharacteristic
21C2×#14558989C2211yescharacteristic
22C2×#14558989C2211yescharacteristic
23C2×#14558989C2211yescharacteristic
24C2×#14558989C2211yescharacteristic
25#18012736C2211yescharacteristic
26#18012728—21no—
27#18012727C2211yescharacteristic
28#18012727C2211yescharacteristic
29#18012724—21no—
30#18012724—21no—
31C4×Dic302C2211yescharacteristic
32C4×D604C2211yescharacteristic
33C4×D604C2211yescharacteristic
34#18012701—21no—
35#18012672C2211yescharacteristic
36C4⋊(C151⋊C8)C2211yescharacteristic
37C4⋊(C151⋊C8)C2211yescharacteristic
38C4⋊(C151⋊C8)C2211yescharacteristic
39#18012663C2211yescharacteristic
40#18012662C2211yescharacteristic
41#18012660C2211yescharacteristic
42#18012660C2211yescharacteristic
43#18012659C2211yescharacteristic
44#18012659C2211yescharacteristic
45#18012650C2211yescharacteristic
46#18012650C2211yescharacteristic
47C4×C151⋊C8C2211yescharacteristic
48#127×C151C2211yescharacteristic
49#124×C151—21no—
50#124×C151C2211yescharacteristic
51#124×C151C2211yescharacteristic
52#123×C151—21no—
53#123×C151—21no—
54C4×Q8×C151C2211yescharacteristic
55C4×Q8×C151C2211yescharacteristic
56C4×D4×C151—21no—
57C4×D4×C151C2211yescharacteristic
58C4×D4×C151C2211yescharacteristic
59C2×Dic302C2311yescharacteristic
60C2×D604—21no—
61C2×D604—21no—
62C2×D604C2311yescharacteristic
63C2×D604C2311yescharacteristic
64C2×C4×D151—21no—
65C2×C4×D151—21no—
66#14558994—41no—
67#14558992—22no—
68#14558992—41no—
69#14558991—22no—
70#14558991—41no—
71#14558989—22no—
72#14558989—41no—
73#14558989—41no—
74#14558989—41no—
75C2×C151⋊C8C2311yescharacteristic
76C2×C151⋊C8C2311yescharacteristic
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C4⋊Dic151C2311yescharacteristic
80Dic151⋊C4—21no—
81(C2×D151)⋊C4—21no—
82(C2×D151)⋊C4—21no—
83(C2×D151)⋊C4—21no—
84(C2×D151)⋊C4—21no—
85(C2×D151)⋊C4—21no—
86(C2×D151)⋊C4—21no—
87C4×Dic151—21no—
88C2×Q8×C151D411yescharacteristic
89C2×Q8×C151C2311yescharacteristic
90C2×D4×C151—21no—
91C2×D4×C151—21no—
92C2×D4×C151C2311yescharacteristic
93C2×D4×C151C2311yescharacteristic
94C22×C4×C151—21no—
95C22×C4×C151—21no—
96C4⋊C4×C151—21no—
97C4⋊C4×C151D411yescharacteristic
98C4⋊C4×C151D411yescharacteristic
99C4⋊C4×C151D411yescharacteristic
100C4⋊C4×C151C2311yescharacteristic
101C22⋊C4×C151—21no—
102C22⋊C4×C151—21no—
103C22⋊C4×C151—21no—
104C22⋊C4×C151—21no—
105C22⋊C4×C151—21no—
106C22⋊C4×C151—21no—
107C42×C151—21no—
108C42×C151C2311yescharacteristic
109C42×C151C2311yescharacteristic
110C42×C151C2311yescharacteristic
111C22×D151—21no—
112C22×D151—21no—
113Dic302—21no—
114Dic302—21no—
115D604—21no—
116D604—21no—
117D604—21no—
118D604—21no—
119D604—42no—
120D604—81no—
121C2×Dic151—21no—
122C2×Dic151—21no—
123C4×D151—81no—
124C4×D151—81no—
125C151⋊C8—21no—
126C151⋊C8—21no—
127C151⋊C8—21no—
128C151⋊C8#4112yes—
129C23×C151—21no—
130C23×C151—21no—
131Q8×C151—21no—
132Q8×C151—21no—
133Q8×C151—41no—
134D4×C151—21no—
135D4×C151—21no—
136D4×C151—21no—
137D4×C151—21no—
138D4×C151—42no—
139D4×C151—81no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—81no—
143C2×C4×C151—81no—
144C2×C4×C151C2×D411yescharacteristic
145C2×C4×C151C2×D411yescharacteristic
146C2×C4×C151C2×D411yescharacteristic
147C2×C4×C151C2×D411yescharacteristic
148C2×C4×C151C2×D411yescharacteristic
149C2×C4×C151C2×D411yescharacteristic
150C2×C4×C151C2411yescharacteristic
151C22×C151—41no—
152C22×C151—41no—
153C22×C151—41no—
154C22×C151—41no—
155C22×C151—41no—
156C22×C151—41no—
157C22×C151C22×D411yescharacteristic
158C2×D151—41no—
159C2×D151—41no—
160C2×D151—41no—
161C2×D151—41no—
162C2×D151—41no—
163C2×D151—41no—
164C4×C151—21no—
165C4×C151—21no—
166C4×C151—21no—
167C4×C151—21no—
168C4×C151—21no—
169C4×C151—21no—
170C4×C151—41no—
171C4×C151—41no—
172C4×C151C2×#4111yescharacteristic
173C4×C151H(5,𝔽2)11yescharacteristic
174Dic151—41no—
175Dic151—41no—
176C2×C151—81no—
177C2×C151—81no—
178C2×C151#55011yescharacteristic
179C2×C151#57511yescharacteristic
180C2×C151#57611yescharacteristic
181D151—81no—
182D151—81no—
183C151#340311yescharacteristic, complemented, Sylow
184#3403—1511nomaximal, Sylow
185#559—1511no—
186#559D15111yescharacteristic, complemented
187#496—1511no—
188#496—1511no—
189#495—1511no—
190#464—1511no—
191#464—1511no—
192#463—1511no—
193#463—1511no—
194#459—1511no—
195#459—1511no—
196#446—1511no—
197#440—1511no—
198#440—1511no—
199C4×D8—1511no—
200C2×Q16—1511no—
201C2×SD16—1511no—
202C2×SD16—1511no—
203C2×SD16—1511no—
204C2×SD16—1511no—
205C2×D8—1511no—
206C2×D8—1511no—
207C2×D8—1511no—
208C2×D8—1511no—
209#127—1511no—
210#127C2×D15111yescharacteristic
211#124—21no—
212#124—3021no—
213#124—1511no—
214#124—1511no—
215#124C2×D15111yescharacteristic
216#124C2×D15111yescharacteristic
217#123—21no—
218#123—21no—
219#123—3021no—
220#123—3021no—
221C4×Q8—1511no—
222C4×Q8C2×D15111yescharacteristic
223C4×Q8C2×D15111yescharacteristic
224C4×D4—21no—
225C4×D4—3021no—
226C4×D4—1511no—
227C4×D4—1511no—
228C4×D4C2×D15111yescharacteristic
229C4×D4C2×D15111yescharacteristic
230#107—1511no—
231C4⋊C8—1511no—
232C4⋊C8—1511no—
233C4⋊C8—1511no—
234#103—1511no—
235#103—1511no—
236#102—1511no—
237#102—1511no—
238#102—1511no—
239#102—1511no—
240#97—1511no—
241#97—1511no—
242C4×C8—1511no—
243C2×Q8—1511no—
244C2×Q8C22⋊D15111yescharacteristic
245C2×Q8C22×D15111yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—3021no—
249C2×D4—3021no—
250C2×D4—1511no—
251C2×D4—1511no—
252C2×D4C22×D15111yescharacteristic
253C2×D4C22×D15111yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—3021no—
257C22×C4—3021no—
258Q16—6041no—
259SD16—3022no—
260SD16—3022no—
261SD16—6041no—
262SD16—6041no—
263D8—3022no—
264D8—6041no—
265D8—6041no—
266D8—6041no—
267C2×C8—1511no—
268C2×C8—1511no—
269C2×C8—1511no—
270C2×C8—1511no—
271C4⋊C4—21no—
272C4⋊C4—3021no—
273C4⋊C4—1511no—
274C4⋊C4C22⋊D15111yescharacteristic
275C4⋊C4C22⋊D15111yescharacteristic
276C4⋊C4C22⋊D15111yescharacteristic
277C4⋊C4C22×D15111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—3021no—
285C22⋊C4—3021no—
286C22⋊C4—3021no—
287C22⋊C4—3021no—
288C22⋊C4—3021no—
289C22⋊C4—3021no—
290C42—21no—
291C42—3021no—
292C42C22×D15111yescharacteristic
293C42C22×D15111yescharacteristic
294C42C22×D15111yescharacteristic
295C23—21no—
296C23—21no—
297C23—3021no—
298C23—3021no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—3021no—
303Q8—3021no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—3021no—
311D4—3021no—
312D4—3021no—
313D4—3021no—
314D4—6042no—
315D4—12081no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—3021no—
321C2×C4—3021no—
322C2×C4—12081no—
323C2×C4—12081no—
324C2×C4C2×C22⋊D15111yescharacteristic
325C2×C4C2×C22⋊D15111yescharacteristic
326C2×C4C2×C22⋊D15111yescharacteristic
327C2×C4C2×C22⋊D15111yescharacteristic
328C2×C4C2×C22⋊D15111yescharacteristic
329C2×C4C2×C22⋊D15111yescharacteristic
330C2×C4C23×D15111yescharacteristic
331C8—3021no—
332C8—3021no—
333C8—3021no—
334C8—1512no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—6041no—
342C22—6041no—
343C22—6041no—
344C22—6041no—
345C22—6041no—
346C22—6041no—
347C22C22×C22⋊D15111yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—6041no—
357C4—6041no—
358C4#41×D15111yescharacteristic
359C4#1801278511yescharacteristic
360C2—81no—
361C2—81no—
362C2—12081no—
363C2—12081no—
364C2#2375288111yescharacteristic
365C2#2375301011yescharacteristic
366C2#2375301511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#559×C151C2
socleC22×C151C22×D4
hypercenter#559D151
hypocenterC151#3403
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23752947C2semidirect
2. #23752602C2semidirect
3. #23752599C2semidirect
4. #23752594C2semidirect
5. #23752434C2semidirect
6. #23752431C2semidirect
7. #23752427C2semidirect
8. #23752424C2semidirect
9. #23752407C2semidirect
10. #23752404C2semidirect
11. #23752343C2semidirect
12. #23752312C2semidirect
13. #23752310C2semidirect
14. C4×#14558989C2semidirect
15. #559×C151C2semidirect
183. C151#3403semidirect
186. #559D151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237529472
#237526022
#237525992
#237525942
#237524342
#237524312
#237524272
#237524242
#237524072
#237524042
#237523432
#237523122
#237523102
C4×#145589892
#559×C1512
#3403151